Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3344,2,Mod(1,3344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3344.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3344 = 2^{4} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3344.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(26.7019744359\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.744786576.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - x^{5} - 17x^{4} + 13x^{3} + 69x^{2} - 21x - 30 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 836) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.27915\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3344.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.27915 | −1.89322 | −0.946609 | − | 0.322383i | \(-0.895516\pi\) | ||||
−0.946609 | + | 0.322383i | \(0.895516\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.53478 | 1.58080 | 0.790400 | − | 0.612591i | \(-0.209873\pi\) | ||||
0.790400 | + | 0.612591i | \(0.209873\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.34459 | 0.886172 | 0.443086 | − | 0.896479i | \(-0.353884\pi\) | ||||
0.443086 | + | 0.896479i | \(0.353884\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.75283 | 2.58428 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.44101 | −1.50906 | −0.754532 | − | 0.656263i | \(-0.772136\pi\) | ||||
−0.754532 | + | 0.656263i | \(0.772136\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −11.5911 | −2.99280 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.37635 | 0.818886 | 0.409443 | − | 0.912336i | \(-0.365723\pi\) | ||||
0.409443 | + | 0.912336i | \(0.365723\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.68827 | −1.67772 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.78459 | 1.20617 | 0.603086 | − | 0.797676i | \(-0.293938\pi\) | ||||
0.603086 | + | 0.797676i | \(0.293938\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.49465 | 1.49893 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −15.5853 | −2.99938 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.19463 | 1.70740 | 0.853700 | − | 0.520766i | \(-0.174353\pi\) | ||||
0.853700 | + | 0.520766i | \(0.174353\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.59107 | 1.72261 | 0.861304 | − | 0.508091i | \(-0.169649\pi\) | ||||
0.861304 | + | 0.508091i | \(0.169649\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.27915 | −0.570827 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.28761 | 1.40086 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.58617 | −1.08276 | −0.541380 | − | 0.840778i | \(-0.682098\pi\) | ||||
−0.541380 | + | 0.840778i | \(0.682098\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 17.8419 | 2.85699 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.37145 | 0.370359 | 0.185179 | − | 0.982705i | \(-0.440713\pi\) | ||||
0.185179 | + | 0.982705i | \(0.440713\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.18026 | −0.179988 | −0.0899941 | − | 0.995942i | \(-0.528685\pi\) | ||||
−0.0899941 | + | 0.995942i | \(0.528685\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 27.4045 | 4.08523 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.69320 | −0.246979 | −0.123490 | − | 0.992346i | \(-0.539409\pi\) | ||||
−0.123490 | + | 0.992346i | \(0.539409\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.50289 | −0.214698 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.0716 | −1.55033 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.51125 | 0.344947 | 0.172474 | − | 0.985014i | \(-0.444824\pi\) | ||||
0.172474 | + | 0.985014i | \(0.444824\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.53478 | 0.476629 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.27915 | −0.434334 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.83925 | 0.630016 | 0.315008 | − | 0.949089i | \(-0.397993\pi\) | ||||
0.315008 | + | 0.949089i | \(0.397993\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.62786 | −0.976647 | −0.488324 | − | 0.872663i | \(-0.662391\pi\) | ||||
−0.488324 | + | 0.872663i | \(0.662391\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 18.1772 | 2.29012 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −19.2328 | −2.38553 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.22139 | −0.271386 | −0.135693 | − | 0.990751i | \(-0.543326\pi\) | ||||
−0.135693 | + | 0.990751i | \(0.543326\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −18.9686 | −2.28355 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.0379 | −1.30996 | −0.654978 | − | 0.755648i | \(-0.727322\pi\) | ||||
−0.654978 | + | 0.755648i | \(0.727322\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.9944 | −1.75496 | −0.877482 | − | 0.479610i | \(-0.840778\pi\) | ||||
−0.877482 | + | 0.479610i | \(0.840778\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −24.5761 | −2.83780 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.34459 | 0.267191 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.18195 | 0.583015 | 0.291507 | − | 0.956569i | \(-0.405843\pi\) | ||||
0.291507 | + | 0.956569i | \(0.405843\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 27.8479 | 3.09421 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.24982 | 0.466478 | 0.233239 | − | 0.972419i | \(-0.425068\pi\) | ||||
0.233239 | + | 0.972419i | \(0.425068\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.9347 | 1.29450 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −30.1506 | −3.23248 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.09139 | 0.645686 | 0.322843 | − | 0.946453i | \(-0.395361\pi\) | ||||
0.322843 | + | 0.946453i | \(0.395361\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.7569 | −1.33729 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −31.4506 | −3.26127 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.53478 | 0.362661 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.16698 | −0.626162 | −0.313081 | − | 0.949726i | \(-0.601361\pi\) | ||||
−0.313081 | + | 0.949726i | \(0.601361\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.75283 | 0.779189 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.86510 | 0.683103 | 0.341551 | − | 0.939863i | \(-0.389048\pi\) | ||||
0.341551 | + | 0.939863i | \(0.389048\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.8156 | −1.26276 | −0.631380 | − | 0.775473i | \(-0.717511\pi\) | ||||
−0.631380 | + | 0.775473i | \(0.717511\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −27.1763 | −2.65214 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.49076 | −0.337465 | −0.168732 | − | 0.985662i | \(-0.553967\pi\) | ||||
−0.168732 | + | 0.985662i | \(0.553967\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.9904 | 1.91473 | 0.957366 | − | 0.288877i | \(-0.0932817\pi\) | ||||
0.957366 | + | 0.288877i | \(0.0932817\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 21.5971 | 2.04990 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.0212 | 1.31900 | 0.659502 | − | 0.751703i | \(-0.270767\pi\) | ||||
0.659502 | + | 0.751703i | \(0.270767\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 20.4473 | 1.90672 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −42.1832 | −3.89984 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.91617 | 0.725674 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.77636 | −0.701171 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.81804 | 0.788710 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.54742 | 0.492254 | 0.246127 | − | 0.969238i | \(-0.420842\pi\) | ||||
0.246127 | + | 0.969238i | \(0.420842\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.87026 | 0.340757 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.6672 | 1.01937 | 0.509685 | − | 0.860361i | \(-0.329762\pi\) | ||||
0.509685 | + | 0.860361i | \(0.329762\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.34459 | 0.203302 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −55.0904 | −4.74143 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.82797 | −0.241610 | −0.120805 | − | 0.992676i | \(-0.538548\pi\) | ||||
−0.120805 | + | 0.992676i | \(0.538548\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.4993 | −1.31464 | −0.657318 | − | 0.753614i | \(-0.728309\pi\) | ||||
−0.657318 | + | 0.753614i | \(0.728309\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.55227 | 0.467585 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.44101 | −0.455000 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 32.5010 | 2.69906 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.92820 | 0.406471 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.234586 | −0.0192180 | −0.00960900 | − | 0.999954i | \(-0.503059\pi\) | ||||
−0.00960900 | + | 0.999954i | \(0.503059\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.3110 | −1.40875 | −0.704375 | − | 0.709828i | \(-0.748773\pi\) | ||||
−0.704375 | + | 0.709828i | \(0.748773\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 26.1763 | 2.11623 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 33.9023 | 2.72310 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.8360 | −0.864806 | −0.432403 | − | 0.901680i | \(-0.642334\pi\) | ||||
−0.432403 | + | 0.901680i | \(0.642334\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.23478 | −0.653060 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.5625 | 1.06888 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.95716 | 0.701579 | 0.350789 | − | 0.936454i | \(-0.385913\pi\) | ||||
0.350789 | + | 0.936454i | \(0.385913\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −11.5911 | −0.902364 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.1193 | 1.09258 | 0.546291 | − | 0.837596i | \(-0.316039\pi\) | ||||
0.546291 | + | 0.837596i | \(0.316039\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.6046 | 1.27728 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.75283 | 0.592874 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.56411 | 0.194946 | 0.0974729 | − | 0.995238i | \(-0.468924\pi\) | ||||
0.0974729 | + | 0.995238i | \(0.468924\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 17.5719 | 1.32831 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −15.8686 | −1.19276 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.455979 | −0.0340815 | −0.0170407 | − | 0.999855i | \(-0.505424\pi\) | ||||
−0.0170407 | + | 0.999855i | \(0.505424\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.41804 | −0.625708 | −0.312854 | − | 0.949801i | \(-0.601285\pi\) | ||||
−0.312854 | + | 0.949801i | \(0.601285\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 25.0129 | 1.84901 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −23.2807 | −1.71163 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.37635 | 0.246903 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −36.5411 | −2.65797 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.9694 | −1.30022 | −0.650110 | − | 0.759840i | \(-0.725277\pi\) | ||||
−0.650110 | + | 0.759840i | \(0.725277\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.2504 | 1.24171 | 0.620854 | − | 0.783926i | \(-0.286786\pi\) | ||||
0.620854 | + | 0.783926i | \(0.286786\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 63.0671 | 4.51633 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.88359 | −0.490435 | −0.245218 | − | 0.969468i | \(-0.578859\pi\) | ||||
−0.245218 | + | 0.969468i | \(0.578859\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.0531 | 1.06708 | 0.533542 | − | 0.845773i | \(-0.320860\pi\) | ||||
0.533542 | + | 0.845773i | \(0.320860\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.28429 | 0.513794 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 21.5576 | 1.51305 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.38256 | 0.585464 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 44.8470 | 3.11708 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.2475 | −1.32505 | −0.662526 | − | 0.749039i | \(-0.730516\pi\) | ||||
−0.662526 | + | 0.749039i | \(0.730516\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 36.1949 | 2.48003 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.17196 | −0.284525 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 22.4871 | 1.52653 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 49.1690 | 3.32253 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.3708 | −1.23575 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.6477 | 1.04785 | 0.523923 | − | 0.851765i | \(-0.324468\pi\) | ||||
0.523923 | + | 0.851765i | \(0.324468\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 58.1048 | 3.87365 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 25.9837 | 1.72460 | 0.862300 | − | 0.506398i | \(-0.169023\pi\) | ||||
0.862300 | + | 0.506398i | \(0.169023\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.9887 | −1.32089 | −0.660445 | − | 0.750874i | \(-0.729632\pi\) | ||||
−0.660445 | + | 0.750874i | \(0.729632\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.68827 | −0.505851 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.7578 | 1.09784 | 0.548920 | − | 0.835875i | \(-0.315039\pi\) | ||||
0.548920 | + | 0.835875i | \(0.315039\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.98510 | −0.390425 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.9924 | −1.10377 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.69553 | 0.433098 | 0.216549 | − | 0.976272i | \(-0.430520\pi\) | ||||
0.216549 | + | 0.976272i | \(0.430520\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.95052 | 0.640969 | 0.320485 | − | 0.947254i | \(-0.396154\pi\) | ||||
0.320485 | + | 0.947254i | \(0.396154\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −44.5618 | −2.85864 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.31238 | −0.339395 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.44101 | −0.346203 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −13.9358 | −0.883145 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.64146 | −0.166728 | −0.0833639 | − | 0.996519i | \(-0.526566\pi\) | ||||
−0.0833639 | + | 0.996519i | \(0.526566\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.78459 | 0.363674 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −39.1355 | −2.45076 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.24328 | −0.139932 | −0.0699659 | − | 0.997549i | \(-0.522289\pi\) | ||||
−0.0699659 | + | 0.997549i | \(0.522289\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.4419 | −0.959512 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 71.2844 | 4.41239 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.31828 | 0.512927 | 0.256464 | − | 0.966554i | \(-0.417443\pi\) | ||||
0.256464 | + | 0.966554i | \(0.417443\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.87672 | 0.545293 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −19.9746 | −1.22243 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −31.0749 | −1.89467 | −0.947334 | − | 0.320248i | \(-0.896234\pi\) | ||||
−0.947334 | + | 0.320248i | \(0.896234\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.9002 | 1.45184 | 0.725918 | − | 0.687781i | \(-0.241415\pi\) | ||||
0.725918 | + | 0.687781i | \(0.241415\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 41.8320 | 2.53179 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.49465 | 0.451945 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.66668 | −0.100141 | −0.0500705 | − | 0.998746i | \(-0.515945\pi\) | ||||
−0.0500705 | + | 0.998746i | \(0.515945\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 74.3580 | 4.45170 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.3003 | 0.793432 | 0.396716 | − | 0.917941i | \(-0.370150\pi\) | ||||
0.396716 | + | 0.917941i | \(0.370150\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.2362 | −0.786811 | −0.393406 | − | 0.919365i | \(-0.628703\pi\) | ||||
−0.393406 | + | 0.919365i | \(0.628703\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −11.5911 | −0.686596 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.56009 | 0.328202 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.60024 | −0.329426 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 20.2225 | 1.18546 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.08113 | −0.472105 | −0.236052 | − | 0.971740i | \(-0.575854\pi\) | ||||
−0.236052 | + | 0.971740i | \(0.575854\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.1057 | 0.995930 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −15.5853 | −0.904349 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −31.4740 | −1.82019 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.76723 | −0.159501 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −22.5117 | −1.29326 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −26.9628 | −1.54388 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.12730 | 0.235557 | 0.117779 | − | 0.993040i | \(-0.462423\pi\) | ||||
0.117779 | + | 0.993040i | \(0.462423\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 42.0244 | 2.39068 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.7342 | −0.608682 | −0.304341 | − | 0.952563i | \(-0.598436\pi\) | ||||
−0.304341 | + | 0.952563i | \(0.598436\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.22131 | 0.408172 | 0.204086 | − | 0.978953i | \(-0.434578\pi\) | ||||
0.204086 | + | 0.978953i | \(0.434578\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 64.2525 | 3.62022 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.7601 | 0.997506 | 0.498753 | − | 0.866744i | \(-0.333792\pi\) | ||||
0.498753 | + | 0.866744i | \(0.333792\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.19463 | 0.514800 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.4467 | 0.638895 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.37635 | 0.187865 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −40.7785 | −2.26198 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −65.5515 | −3.62501 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.96987 | −0.218866 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.86554 | −0.322399 | −0.161200 | − | 0.986922i | \(-0.551536\pi\) | ||||
−0.161200 | + | 0.986922i | \(0.551536\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −51.0615 | −2.79815 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.85213 | −0.429008 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.27598 | −0.341874 | −0.170937 | − | 0.985282i | \(-0.554680\pi\) | ||||
−0.170937 | + | 0.985282i | \(0.554680\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −45.9776 | −2.49716 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.59107 | 0.519386 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.9358 | −1.07643 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −67.0496 | −3.60983 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.8165 | 0.688025 | 0.344012 | − | 0.938965i | \(-0.388214\pi\) | ||||
0.344012 | + | 0.938965i | \(0.388214\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.94535 | 0.478834 | 0.239417 | − | 0.970917i | \(-0.423044\pi\) | ||||
0.239417 | + | 0.970917i | \(0.423044\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 84.7996 | 4.52627 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 33.8419 | 1.80122 | 0.900611 | − | 0.434626i | \(-0.143119\pi\) | ||||
0.900611 | + | 0.434626i | \(0.143119\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −39.0165 | −2.07078 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −25.9583 | −1.37386 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.70804 | 0.142925 | 0.0714625 | − | 0.997443i | \(-0.477233\pi\) | ||||
0.0714625 | + | 0.997443i | \(0.477233\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.27915 | −0.172111 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −53.0019 | −2.77425 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.5295 | −1.17603 | −0.588016 | − | 0.808850i | \(-0.700091\pi\) | ||||
−0.588016 | + | 0.808850i | \(0.700091\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 18.3855 | 0.957111 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.88786 | 0.305683 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.5197 | 1.32136 | 0.660680 | − | 0.750668i | \(-0.270268\pi\) | ||||
0.660680 | + | 0.750668i | \(0.270268\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −28.9157 | −1.49320 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −50.0281 | −2.57658 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.0860 | 0.620818 | 0.310409 | − | 0.950603i | \(-0.399534\pi\) | ||||
0.310409 | + | 0.950603i | \(0.399534\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.1908 | −0.931944 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.4116 | −0.991885 | −0.495943 | − | 0.868355i | \(-0.665177\pi\) | ||||
−0.495943 | + | 0.868355i | \(0.665177\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.28761 | 0.422376 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.15037 | −0.465139 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.2668 | 0.571250 | 0.285625 | − | 0.958342i | \(-0.407799\pi\) | ||||
0.285625 | + | 0.958342i | \(0.407799\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.5308 | 0.987716 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −38.2586 | −1.92989 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 18.3170 | 0.921630 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.9391 | 0.599204 | 0.299602 | − | 0.954064i | \(-0.403146\pi\) | ||||
0.299602 | + | 0.954064i | \(0.403146\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.68827 | −0.384895 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.90453 | 0.494608 | 0.247304 | − | 0.968938i | \(-0.420455\pi\) | ||||
0.247304 | + | 0.968938i | \(0.420455\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −52.1851 | −2.59953 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 98.4362 | 4.89134 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.58617 | −0.326464 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.1425 | 0.550960 | 0.275480 | − | 0.961307i | \(-0.411163\pi\) | ||||
0.275480 | + | 0.961307i | \(0.411163\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.27336 | 0.457421 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.3461 | 0.558303 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.0222 | 0.737409 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 50.8246 | 2.48889 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.88093 | 0.385009 | 0.192504 | − | 0.981296i | \(-0.438339\pi\) | ||||
0.192504 | + | 0.981296i | \(0.438339\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 37.8040 | 1.84245 | 0.921226 | − | 0.389027i | \(-0.127189\pi\) | ||||
0.921226 | + | 0.389027i | \(0.127189\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13.1271 | −0.638262 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 25.3046 | 1.22745 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.8842 | −0.865478 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 17.8419 | 0.861415 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.80267 | 0.472178 | 0.236089 | − | 0.971731i | \(-0.424134\pi\) | ||||
0.236089 | + | 0.971731i | \(0.424134\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.1855 | −1.06617 | −0.533083 | − | 0.846063i | \(-0.678967\pi\) | ||||
−0.533083 | + | 0.846063i | \(0.678967\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −106.576 | −5.10991 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.78459 | 0.276715 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.9073 | −0.902396 | −0.451198 | − | 0.892424i | \(-0.649003\pi\) | ||||
−0.451198 | + | 0.892424i | \(0.649003\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11.6516 | −0.554840 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.46822 | −0.212292 | −0.106146 | − | 0.994351i | \(-0.533851\pi\) | ||||
−0.106146 | + | 0.994351i | \(0.533851\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 21.5317 | 1.02070 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.769242 | 0.0363839 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.6131 | −1.35033 | −0.675167 | − | 0.737665i | \(-0.735929\pi\) | ||||
−0.675167 | + | 0.737665i | \(0.735929\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.37145 | 0.111667 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 56.7654 | 2.66707 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −45.0930 | −2.11399 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.8196 | −0.693232 | −0.346616 | − | 0.938007i | \(-0.612669\pi\) | ||||
−0.346616 | + | 0.938007i | \(0.612669\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −52.6213 | −2.45615 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 36.4495 | 1.69762 | 0.848811 | − | 0.528697i | \(-0.177319\pi\) | ||||
0.848811 | + | 0.528697i | \(0.177319\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.9591 | 1.53174 | 0.765871 | − | 0.642995i | \(-0.222308\pi\) | ||||
0.765871 | + | 0.642995i | \(0.222308\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −111.171 | −5.15542 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.28650 | −0.290905 | −0.145452 | − | 0.989365i | \(-0.546464\pi\) | ||||
−0.145452 | + | 0.989365i | \(0.546464\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.20826 | −0.240495 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 35.5329 | 1.63727 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.18026 | −0.0542685 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.49465 | 0.343878 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 19.4693 | 0.891439 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.8832 | 0.862797 | 0.431399 | − | 0.902161i | \(-0.358020\pi\) | ||||
0.431399 | + | 0.902161i | \(0.358020\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 35.8354 | 1.63396 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −44.4735 | −2.02362 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −21.7989 | −0.989837 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.5268 | −1.11142 | −0.555708 | − | 0.831377i | \(-0.687553\pi\) | ||||
−0.555708 | + | 0.831377i | \(0.687553\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −29.3719 | −1.32824 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.8056 | 1.57075 | 0.785377 | − | 0.619017i | \(-0.212469\pi\) | ||||
0.785377 | + | 0.619017i | \(0.212469\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 31.0443 | 1.39816 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 27.4045 | 1.23174 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −25.8794 | −1.16085 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.63700 | 0.431411 | 0.215706 | − | 0.976458i | \(-0.430795\pi\) | ||||
0.215706 | + | 0.976458i | \(0.430795\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −46.2992 | −2.06850 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −32.1848 | −1.43505 | −0.717524 | − | 0.696534i | \(-0.754724\pi\) | ||||
−0.717524 | + | 0.696534i | \(0.754724\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.2666 | 1.07985 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −54.4490 | −2.41816 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.3645 | 0.592371 | 0.296185 | − | 0.955131i | \(-0.404285\pi\) | ||||
0.296185 | + | 0.955131i | \(0.404285\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −35.1558 | −1.55520 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −15.5853 | −0.688106 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −45.3004 | −1.99617 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.69320 | −0.0744670 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.40811 | −0.369075 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.8705 | 0.695298 | 0.347649 | − | 0.937625i | \(-0.386980\pi\) | ||||
0.347649 | + | 0.937625i | \(0.386980\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.2073 | 0.752423 | 0.376211 | − | 0.926534i | \(-0.377227\pi\) | ||||
0.376211 | + | 0.926534i | \(0.377227\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −57.6209 | −2.51478 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 32.3828 | 1.41062 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.4615 | 0.454849 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 37.5179 | 1.62814 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.9031 | −0.558896 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.3391 | −0.533465 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.49522 | 0.0645237 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.50289 | −0.0647340 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.0905 | 1.50866 | 0.754330 | − | 0.656496i | \(-0.227962\pi\) | ||||
0.754330 | + | 0.656496i | \(0.227962\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 27.6040 | 1.18460 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 70.6616 | 3.02681 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.78485 | 0.119072 | 0.0595358 | − | 0.998226i | \(-0.481038\pi\) | ||||
0.0595358 | + | 0.998226i | \(0.481038\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −59.1375 | −2.52393 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.19463 | 0.391704 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.1496 | 0.516652 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 76.3408 | 3.24049 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.49963 | 0.105913 | 0.0529564 | − | 0.998597i | \(-0.483136\pi\) | ||||
0.0529564 | + | 0.998597i | \(0.483136\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.42181 | 0.271614 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.0716 | −0.467442 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.06488 | −0.255604 | −0.127802 | − | 0.991800i | \(-0.540792\pi\) | ||||
−0.127802 | + | 0.991800i | \(0.540792\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 49.5618 | 2.08508 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 65.2920 | 2.74201 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.9447 | −0.626513 | −0.313256 | − | 0.949669i | \(-0.601420\pi\) | ||||
−0.313256 | + | 0.949669i | \(0.601420\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.3521 | −1.14465 | −0.572325 | − | 0.820027i | \(-0.693958\pi\) | ||||
−0.572325 | + | 0.820027i | \(0.693958\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 58.9244 | 2.46160 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 43.3535 | 1.80797 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.83560 | −0.0764170 | −0.0382085 | − | 0.999270i | \(-0.512165\pi\) | ||||
−0.0382085 | + | 0.999270i | \(0.512165\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −56.5666 | −2.35083 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.96409 | 0.413380 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.51125 | 0.104005 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −149.108 | −6.16487 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −31.1835 | −1.28708 | −0.643540 | − | 0.765412i | \(-0.722535\pi\) | ||||
−0.643540 | + | 0.765412i | \(0.722535\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.59107 | 0.395193 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 22.5723 | 0.928501 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.4998 | 0.841827 | 0.420913 | − | 0.907101i | \(-0.361710\pi\) | ||||
0.420913 | + | 0.907101i | \(0.361710\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 27.9819 | 1.14715 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −49.3613 | −2.02023 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.8573 | 0.893065 | 0.446532 | − | 0.894768i | \(-0.352659\pi\) | ||||
0.446532 | + | 0.894768i | \(0.352659\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.12818 | 0.0868102 | 0.0434051 | − | 0.999058i | \(-0.486179\pi\) | ||||
0.0434051 | + | 0.999058i | \(0.486179\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −17.2221 | −0.701338 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.53478 | 0.143709 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.3933 | 0.462439 | 0.231219 | − | 0.972902i | \(-0.425729\pi\) | ||||
0.231219 | + | 0.972902i | \(0.425729\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −70.6908 | −2.86454 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.21273 | 0.372707 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −44.3930 | −1.79302 | −0.896508 | − | 0.443028i | \(-0.853904\pi\) | ||||
−0.896508 | + | 0.443028i | \(0.853904\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −27.4877 | −1.10841 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 37.3951 | 1.50547 | 0.752736 | − | 0.658323i | \(-0.228734\pi\) | ||||
0.752736 | + | 0.658323i | \(0.228734\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.6910 | 0.630673 | 0.315337 | − | 0.948980i | \(-0.397883\pi\) | ||||
0.315337 | + | 0.948980i | \(0.397883\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −90.1544 | −3.61777 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14.2818 | 0.572189 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.30344 | −0.252138 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.27915 | −0.130957 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −22.2372 | −0.886657 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.72618 | 0.307574 | 0.153787 | − | 0.988104i | \(-0.450853\pi\) | ||||
0.153787 | + | 0.988104i | \(0.450853\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 63.1154 | 2.50861 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19.6089 | 0.778155 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.17723 | 0.323994 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −85.5749 | −3.38529 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.26960 | −0.287132 | −0.143566 | − | 0.989641i | \(-0.545857\pi\) | ||||
−0.143566 | + | 0.989641i | \(0.545857\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.00629 | 0.236865 | 0.118432 | − | 0.992962i | \(-0.462213\pi\) | ||||
0.118432 | + | 0.992962i | \(0.462213\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13.6805 | 0.538669 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −46.0802 | −1.81160 | −0.905801 | − | 0.423704i | \(-0.860730\pi\) | ||||
−0.905801 | + | 0.423704i | \(0.860730\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.83925 | 0.189957 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −73.7388 | −2.89005 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −37.2226 | −1.45663 | −0.728317 | − | 0.685240i | \(-0.759697\pi\) | ||||
−0.728317 | + | 0.685240i | \(0.759697\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 41.2410 | 1.61142 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −116.249 | −4.53531 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −34.9204 | −1.36030 | −0.680152 | − | 0.733071i | \(-0.738086\pi\) | ||||
−0.680152 | + | 0.733071i | \(0.738086\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.6194 | −0.724211 | −0.362105 | − | 0.932137i | \(-0.617942\pi\) | ||||
−0.362105 | + | 0.932137i | \(0.617942\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 60.2405 | 2.33955 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.28761 | 0.321380 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 53.1872 | 2.05942 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −51.3111 | −1.98380 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.62786 | −0.294470 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −39.6581 | −1.52871 | −0.764355 | − | 0.644796i | \(-0.776942\pi\) | ||||
−0.764355 | + | 0.644796i | \(0.776942\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −116.806 | −4.49587 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −43.8777 | −1.68636 | −0.843179 | − | 0.537632i | \(-0.819319\pi\) | ||||
−0.843179 | + | 0.537632i | \(0.819319\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.4591 | −0.554888 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −85.2046 | −3.26505 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.57257 | 0.213228 | 0.106614 | − | 0.994300i | \(-0.465999\pi\) | ||||
0.106614 | + | 0.994300i | \(0.465999\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.99626 | −0.381937 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 65.5460 | 2.50073 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.6638 | −0.520547 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.03739 | 0.115548 | 0.0577739 | − | 0.998330i | \(-0.481600\pi\) | ||||
0.0577739 | + | 0.998330i | \(0.481600\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 18.1772 | 0.690496 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −54.7866 | −2.07818 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.00687 | 0.303282 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −54.9514 | −2.07845 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.85374 | 0.258862 | 0.129431 | − | 0.991588i | \(-0.458685\pi\) | ||||
0.129431 | + | 0.991588i | \(0.458685\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.58617 | −0.248402 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 19.6260 | 0.739159 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16.0959 | 0.605347 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.4947 | 0.844804 | 0.422402 | − | 0.906409i | \(-0.361187\pi\) | ||||
0.422402 | + | 0.906409i | \(0.361187\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 40.1748 | 1.50667 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 55.4805 | 2.07776 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −19.2328 | −0.719264 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −21.9557 | −0.819949 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.5930 | −0.618816 | −0.309408 | − | 0.950929i | \(-0.600131\pi\) | ||||
−0.309408 | + | 0.950929i | \(0.600131\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30.0474 | −1.11902 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −32.6293 | −1.21350 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 68.9105 | 2.55927 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.7104 | −0.471402 | −0.235701 | − | 0.971826i | \(-0.575739\pi\) | ||||
−0.235701 | + | 0.971826i | \(0.575739\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 62.5811 | 2.31782 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.98498 | −0.147390 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.8202 | −0.732077 | −0.366039 | − | 0.930600i | \(-0.619286\pi\) | ||||
−0.366039 | + | 0.930600i | \(0.619286\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 17.4201 | 0.642550 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.22139 | −0.0818261 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 48.1166 | 1.77000 | 0.885000 | − | 0.465592i | \(-0.154158\pi\) | ||||
0.885000 | + | 0.465592i | \(0.154158\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17.8419 | 0.655438 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −35.5155 | −1.30294 | −0.651468 | − | 0.758676i | \(-0.725847\pi\) | ||||
−0.651468 | + | 0.758676i | \(0.725847\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.829208 | −0.0303798 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 32.9481 | 1.20551 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.18441 | −0.299052 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.43033 | 0.307627 | 0.153814 | − | 0.988100i | \(-0.450844\pi\) | ||||
0.153814 | + | 0.988100i | \(0.450844\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.66176 | 0.315652 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −61.1906 | −2.22695 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39.6118 | −1.43972 | −0.719858 | − | 0.694121i | \(-0.755793\pi\) | ||||
−0.719858 | + | 0.694121i | \(0.755793\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −18.9686 | −0.688515 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −40.8269 | −1.47998 | −0.739988 | − | 0.672621i | \(-0.765169\pi\) | ||||
−0.739988 | + | 0.672621i | \(0.765169\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 46.8693 | 1.69678 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 92.5274 | 3.34534 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −26.3304 | −0.950735 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.64570 | −0.275711 | −0.137856 | − | 0.990452i | \(-0.544021\pi\) | ||||
−0.137856 | + | 0.990452i | \(0.544021\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.35604 | 0.264921 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.7578 | −0.458867 | −0.229433 | − | 0.973324i | \(-0.573687\pi\) | ||||
−0.229433 | + | 0.973324i | \(0.573687\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 71.8817 | 2.58207 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 50.6363 | 1.81657 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.37145 | 0.0849662 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.0379 | −0.394967 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −143.301 | −5.12115 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −38.3028 | −1.36709 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −27.0124 | −0.962889 | −0.481445 | − | 0.876476i | \(-0.659888\pi\) | ||||
−0.481445 | + | 0.876476i | \(0.659888\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −27.2769 | −0.971084 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 32.8740 | 1.16886 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 41.5033 | 1.47382 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −29.1081 | −1.03236 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.2729 | −0.611837 | −0.305919 | − | 0.952058i | \(-0.598964\pi\) | ||||
−0.305919 | + | 0.952058i | \(0.598964\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.71685 | −0.202248 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 47.2255 | 1.66863 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14.9944 | −0.529141 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 47.9405 | 1.68968 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 101.899 | 3.58702 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −38.7686 | −1.36303 | −0.681515 | − | 0.731804i | \(-0.738679\pi\) | ||||
−0.681515 | + | 0.731804i | \(0.738679\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.4408 | −0.542199 | −0.271100 | − | 0.962551i | \(-0.587387\pi\) | ||||
−0.271100 | + | 0.962551i | \(0.587387\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −78.3725 | −2.74864 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 31.6616 | 1.10906 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.18026 | −0.0412921 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −98.9025 | −3.45593 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 34.9424 | 1.21950 | 0.609750 | − | 0.792594i | \(-0.291270\pi\) | ||||
0.609750 | + | 0.792594i | \(0.291270\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.9332 | 0.729684 | 0.364842 | − | 0.931069i | \(-0.381123\pi\) | ||||
0.364842 | + | 0.931069i | \(0.381123\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −24.5761 | −0.855630 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31.8329 | −1.10694 | −0.553470 | − | 0.832869i | \(-0.686697\pi\) | ||||
−0.553470 | + | 0.832869i | \(0.686697\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.1128 | −0.524891 | −0.262445 | − | 0.964947i | \(-0.584529\pi\) | ||||
−0.262445 | + | 0.964947i | \(0.584529\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.46529 | 0.189589 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.07428 | −0.175813 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 49.9085 | 1.72715 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −149.479 | −5.16676 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −39.0512 | −1.34820 | −0.674099 | − | 0.738641i | \(-0.735468\pi\) | ||||
−0.674099 | + | 0.738641i | \(0.735468\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 55.5412 | 1.91521 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −43.6139 | −1.50214 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 58.6935 | 2.01912 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.34459 | 0.0805611 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 43.4036 | 1.48961 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −38.0983 | −1.30599 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.8573 | −0.508703 | −0.254351 | − | 0.967112i | \(-0.581862\pi\) | ||||
−0.254351 | + | 0.967112i | \(0.581862\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 27.4045 | 0.937216 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42.3513 | 1.44669 | 0.723347 | − | 0.690485i | \(-0.242603\pi\) | ||||
0.723347 | + | 0.690485i | \(0.242603\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.9371 | −0.816723 | −0.408361 | − | 0.912820i | \(-0.633900\pi\) | ||||
−0.408361 | + | 0.912820i | \(0.633900\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −18.2324 | −0.621358 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 41.0021 | 1.39573 | 0.697865 | − | 0.716230i | \(-0.254134\pi\) | ||||
0.697865 | + | 0.716230i | \(0.254134\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.06357 | 0.308171 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 18.3640 | 0.623676 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.18195 | 0.175786 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.0866 | 0.409540 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −47.8116 | −1.61818 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 20.6747 | 0.698933 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.31855 | −0.0445242 | −0.0222621 | − | 0.999752i | \(-0.507087\pi\) | ||||
−0.0222621 | + | 0.999752i | \(0.507087\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 26.4992 | 0.893797 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.5816 | −0.861865 | −0.430933 | − | 0.902384i | \(-0.641815\pi\) | ||||
−0.430933 | + | 0.902384i | \(0.641815\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.2089 | 0.781040 | 0.390520 | − | 0.920594i | \(-0.372295\pi\) | ||||
0.390520 | + | 0.920594i | \(0.372295\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −56.0920 | −1.88551 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 33.6865 | 1.13108 | 0.565540 | − | 0.824721i | \(-0.308668\pi\) | ||||
0.565540 | + | 0.824721i | \(0.308668\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.0064 | 0.436222 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 27.8479 | 0.932941 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.69320 | −0.0566609 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.61179 | −0.0538760 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 103.208 | 3.44602 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 88.1863 | 2.94118 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.47887 | 0.282472 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.07417 | 0.301969 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −29.7559 | −0.989119 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −40.5536 | −1.34656 | −0.673280 | − | 0.739388i | \(-0.735115\pi\) | ||||
−0.673280 | + | 0.739388i | \(0.735115\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 53.2240 | 1.76533 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.4247 | 0.477911 | 0.238956 | − | 0.971031i | \(-0.423195\pi\) | ||||
0.238956 | + | 0.971031i | \(0.423195\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.24982 | 0.140648 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 88.4150 | 2.92291 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 27.3549 | 0.903337 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −39.7419 | −1.31096 | −0.655482 | − | 0.755211i | \(-0.727534\pi\) | ||||
−0.655482 | + | 0.755211i | \(0.727534\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.5340 | −0.445962 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 60.0573 | 1.97681 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −49.3611 | −1.62298 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −99.3574 | −3.26332 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20.4506 | −0.670964 | −0.335482 | − | 0.942047i | \(-0.608899\pi\) | ||||
−0.335482 | + | 0.942047i | \(0.608899\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.50289 | −0.0492552 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 35.1991 | 1.15237 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11.9347 | 0.390305 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.32869 | −0.272086 | −0.136043 | − | 0.990703i | \(-0.543439\pi\) | ||||
−0.136043 | + | 0.990703i | \(0.543439\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −23.6798 | −0.772760 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 51.0299 | 1.66353 | 0.831763 | − | 0.555131i | \(-0.187332\pi\) | ||||
0.831763 | + | 0.555131i | \(0.187332\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.7179 | 0.446716 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −129.165 | −4.20172 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.5652 | 0.733270 | 0.366635 | − | 0.930365i | \(-0.380510\pi\) | ||||
0.366635 | + | 0.930365i | \(0.380510\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 81.5848 | 2.64835 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −58.2380 | −1.88850 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 34.1812 | 1.10724 | 0.553619 | − | 0.832770i | \(-0.313246\pi\) | ||||
0.553619 | + | 0.832770i | \(0.313246\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −63.5178 | −2.05539 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −30.1506 | −0.974630 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.63045 | −0.214108 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 60.9886 | 1.96738 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −27.0633 | −0.872103 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 60.9762 | 1.96289 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.0673 | −0.709636 | −0.354818 | − | 0.934935i | \(-0.615457\pi\) | ||||
−0.354818 | + | 0.934935i | \(0.615457\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11.0716 | −0.355670 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.2403 | −0.424902 | −0.212451 | − | 0.977172i | \(-0.568145\pi\) | ||||
−0.212451 | + | 0.977172i | \(0.568145\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −36.3396 | −1.16499 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 133.719 | 4.28243 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.65904 | 0.213041 | 0.106521 | − | 0.994310i | \(-0.466029\pi\) | ||||
0.106521 | + | 0.994310i | \(0.466029\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.09139 | 0.194682 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 154.982 | 4.94820 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.9907 | −0.988449 | −0.494225 | − | 0.869334i | \(-0.664548\pi\) | ||||
−0.494225 | + | 0.869334i | \(0.664548\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.3319 | −0.775280 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 13.0178 | 0.414361 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.82733 | −0.217097 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −59.2229 | −1.88128 | −0.940639 | − | 0.339408i | \(-0.889773\pi\) | ||||
−0.940639 | + | 0.339408i | \(0.889773\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19.2340 | 0.610373 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 53.2093 | 1.68685 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.5785 | −0.905092 | −0.452546 | − | 0.891741i | \(-0.649484\pi\) | ||||
−0.452546 | + | 0.891741i | \(0.649484\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 102.647 | 3.24761 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3344.2.a.w.1.1 | 6 | ||
4.3 | odd | 2 | 836.2.a.e.1.6 | ✓ | 6 | ||
12.11 | even | 2 | 7524.2.a.q.1.1 | 6 | |||
44.43 | even | 2 | 9196.2.a.n.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
836.2.a.e.1.6 | ✓ | 6 | 4.3 | odd | 2 | ||
3344.2.a.w.1.1 | 6 | 1.1 | even | 1 | trivial | ||
7524.2.a.q.1.1 | 6 | 12.11 | even | 2 | |||
9196.2.a.n.1.6 | 6 | 44.43 | even | 2 |